Multi-Access Edge Computing (MEC) and Open Radio Access Network (O-RAN) have emerged as promising paradigms to address diverse applications and service require-ments. MEC brings computational power to the network edge, enabling efficient offloading of compute-intensive tasks, while O-RAN facilitates network disaggregation for centralized deployment. The inherent conflict between MEC's user-centric proximity and O-RAN's disaggregation goals poses challenges in their integration. In this paper, we introduce a comprehensive analytical framework to optimize the integration of RAN dis-aggregation and MEC services. This framework models RAN functions and considers both full and partial task offloading strategies. This collaborative approach aims to minimize costs related to bandwidth usage and computing resource utilization. The simulation results indicate that the integration of MEC can significantly increase network costs. However, this impact can be mitigated by enhancing the centralization of computing resources. Additionally, doubling the weight of the link cost leads to a significant increase in the number of full compared to partial offloading, highlighting the tradeoff between these two strategies regarding computing resources and bandwidth utilization.